Simplify the following expression: $z = \dfrac{4}{9y} + \dfrac{1}{10y}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $9y$ and $10y$ $\lcm(9y, 10y) = 90y$ $ z = \dfrac{10}{10} \cdot \dfrac{4}{9y} + \dfrac{9}{9} \cdot \dfrac{1}{10y} $ $z = \dfrac{40}{90y} + \dfrac{9}{90y}$ $z = \dfrac{40 +9}{90y}$ $z = \dfrac{49}{90y}$